How do you write the area a of a circle as a function of its circumference?

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Answer 1 · 2015-02-13T14:18:00

We know:

Area of a circle = #A = (pi)r^2#

Circumference of a circle = #C = 2(pi)r#

Where pi is a constant and r is the radius of the circle.

Using these two formulas we can express A in terms of C as follows:

#C^2 = [2(pi)r]^2#

#=> C^2 = 4[(pi)^2]r^2#

#=> C^2 = 4(pi)[(pi)r^2]#

As# (pi)r^2 = A#

#=> C^2 = 4(pi)A#

Therefore:

#A = (C^2)/[4(pi)]#